CASSL.ipynb

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  "metadata": {
    "colab": {
      "name": "CASSL.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k7CySDuzD65G"
      },
      "source": [
        "**Use this notebook if data has missing annotations**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uzxWXO1V2oh6"
      },
      "source": [
        "# Importing libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sXG7u5it2WrK"
      },
      "source": [
        "import math\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import random\n",
        "from sklearn.cluster import KMeans\n",
        "from sklearn.preprocessing import LabelEncoder\n",
        "from sklearn.metrics.cluster import adjusted_rand_score, adjusted_mutual_info_score, fowlkes_mallows_score\n",
        "from sklearn.metrics import silhouette_score, davies_bouldin_score, calinski_harabasz_score\n",
        "import seaborn as sns\n",
        "from sklearn.manifold import TSNE\n",
        "from sklearn.decomposition import NMF\n",
        "import tensorflow as tf\n",
        "from sklearn.metrics.pairwise import euclidean_distances"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "azZAvGkqCVP3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b6b03358-2132-42ee-e0e5-4c111d4714fe"
      },
      "source": [
        "!pip install pytictoc"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting pytictoc\n",
            "  Downloading pytictoc-1.5.2-py2.py3-none-any.whl (4.0 kB)\n",
            "Installing collected packages: pytictoc\n",
            "Successfully installed pytictoc-1.5.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I_g0ZJR-jOi_",
        "outputId": "dcbc7a15-d23d-4695-f749-47d7e961e3c7"
      },
      "source": [
        "!pip install kneed"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting kneed\n",
            "  Downloading kneed-0.7.0-py2.py3-none-any.whl (9.4 kB)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from kneed) (1.4.1)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from kneed) (3.2.2)\n",
            "Requirement already satisfied: numpy>=1.14.2 in /usr/local/lib/python3.7/dist-packages (from kneed) (1.19.5)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->kneed) (2.8.2)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->kneed) (1.3.2)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->kneed) (0.11.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->kneed) (2.4.7)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.1->matplotlib->kneed) (1.15.0)\n",
            "Installing collected packages: kneed\n",
            "Successfully installed kneed-0.7.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i9ks8QJYCe3j"
      },
      "source": [
        "from pytictoc import TicToc\n",
        "t = TicToc()"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CEhM9idP3AuQ"
      },
      "source": [
        "# Importing scRNA-seq data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bRiS4oDCi7aX",
        "outputId": "e47ec65a-72db-4270-fb00-b8e2070b6e09"
      },
      "source": [
        "#Mounting google drive\n",
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vnkqz3ZpjErq",
        "outputId": "21b3779d-3a63-440a-87e9-a7bcf13350e0"
      },
      "source": [
        "ls \"/content/drive/My Drive/scRNASeq_RKM_data/EBI_normalized/\""
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "E-GEOD-130148_Labels.csv  E-GEOD-81547_Labels.csv  ExpDesign-E-GEOD-130148.csv\n",
            "E-GEOD-130148.norm.csv    E-GEOD-81547.norm.csv    ExpDesign-E-GEOD-81547.csv\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A4nNDNWpi4AY"
      },
      "source": [
        "data = pd.read_csv(\"/content/drive/My Drive/scRNASeq_RKM_data/EBI_normalized/E-GEOD-81547.norm.csv\", header=0, index_col=None, sep=\",\")"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T6Dzw-jBcMoH"
      },
      "source": [
        "labels = pd.read_csv(\"/content/drive/My Drive/scRNASeq_RKM_data/EBI_normalized/E-GEOD-81547_Labels.csv\", header=0, index_col=None, sep=\",\")"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5nAz8yYsIjxe"
      },
      "source": [
        "data = data.T"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EPrGapzDjtH_"
      },
      "source": [
        "data.reset_index(inplace=True, drop=True)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 253
        },
        "id": "lp27GOLalq25",
        "outputId": "98cc10dd-d30e-4fda-a0b3-93e9baaff0bc"
      },
      "source": [
        "data.head()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
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              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
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              "      <td>16.423933</td>\n",
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              "      <td>50.868786</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.000000</td>\n",
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              "      <td>1057.993500</td>\n",
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              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 27828 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "        0          1          2         3      ...  27824  27825  27826      27827\n",
              "0    1.930023    0.00000    3.07583  9.751206  ...    0.0    0.0    0.0   0.000000\n",
              "1    0.000000  193.19691  743.46606  8.586529  ...    0.0    0.0    0.0   7.102823\n",
              "2  223.590700    0.00000    0.00000  0.000000  ...    0.0    0.0    0.0   0.000000\n",
              "3   25.825342    0.00000    0.00000  2.335857  ...    0.0    0.0    0.0  50.868786\n",
              "4    0.000000    0.00000    0.00000  0.000000  ...    0.0    0.0    0.0   0.000000\n",
              "\n",
              "[5 rows x 27828 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eM5GWDv_ScjG"
      },
      "source": [
        "# Scaling data (if required)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NFsmycwG3-mO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 253
        },
        "outputId": "81465b40-fd2b-40a3-ed8f-b5ff591e447f"
      },
      "source": [
        "from sklearn.preprocessing import MinMaxScaler\n",
        "scaler = MinMaxScaler()\n",
        "data = pd.DataFrame(scaler.fit_transform(data))\n",
        "data.head()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "      <td>0.011749</td>\n",
              "      <td>0.008596</td>\n",
              "      <td>0.004603</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.058000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.024228</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.001773</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.219403</td>\n",
              "      <td>0.013020</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.309214</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.012990</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.003330</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.331611</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.141995</td>\n",
              "      <td>0.001984</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.02795</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.007678</td>\n",
              "      <td>0.001409</td>\n",
              "      <td>0.087308</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.003843</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.030807</td>\n",
              "      <td>0.039152</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000723</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.260474</td>\n",
              "      <td>0.153469</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.418917</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.073742</td>\n",
              "      <td>0.441027</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.164968</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.019823</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.02052</td>\n",
              "      <td>0.040561</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.091327</td>\n",
              "      <td>0.026901</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.087103</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.001528</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.008929</td>\n",
              "      <td>0.006334</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.665536</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.163593</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.014526</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.087610</td>\n",
              "      <td>0.012078</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.090036</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.015492</td>\n",
              "      <td>0.003352</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.290664</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.002709</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 27828 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "      0        1         2         3      ...  27824  27825  27826     27827\n",
              "0  0.000971  0.00000  0.003468  0.013900  ...    0.0    0.0    0.0  0.000000\n",
              "1  0.000000  0.08763  0.838377  0.012239  ...    0.0    0.0    0.0  0.012162\n",
              "2  0.112468  0.00000  0.000000  0.000000  ...    0.0    0.0    0.0  0.000000\n",
              "3  0.012990  0.00000  0.000000  0.003330  ...    0.0    0.0    0.0  0.087103\n",
              "4  0.000000  0.00000  0.000000  0.000000  ...    0.0    0.0    0.0  0.000000\n",
              "\n",
              "[5 rows x 27828 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PQKgW5eASrlA"
      },
      "source": [
        "# Checking loaded data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pvcCrZtejwjW",
        "outputId": "d96835b9-0678-40c5-e52e-09e7683d7b7b"
      },
      "source": [
        "data.shape"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2544, 27828)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "it-bUYvxj7hd",
        "outputId": "4f1b50fa-ffa4-4f1a-8832-d3ad6772b59e"
      },
      "source": [
        "labels.shape"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2544, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xzLNQ2-yM5a9",
        "outputId": "35654f71-aed2-4a91-f07f-30c1a628cff9"
      },
      "source": [
        "labels.nunique()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Assay      2544\n",
              "Labels        6\n",
              "Labels1       6\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o8_HBdAFdPHx",
        "outputId": "0539612e-8400-432f-820b-1113c31eb7f2"
      },
      "source": [
        "labels = labels['Labels1']\n",
        "labels.head()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    Pancreatic A Cell\n",
              "1    Pancreatic A Cell\n",
              "2          Acinar Cell\n",
              "3    Pancreatic A Cell\n",
              "4    Pancreatic A Cell\n",
              "Name: Labels1, dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nmxn0dEhwf0s"
      },
      "source": [
        "# Finding the optimal dimensions for embedding using reconstruction error"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v7PqelPewzCd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3c994daf-9fdc-4bc2-c6bd-c8e37a28e0e1"
      },
      "source": [
        "d = range(2,16)\n",
        "k=[]\n",
        "error=[]\n",
        "# try each value of k\n",
        "for i in d:\n",
        "    print(\"Applying NMF for k=%d ...\" % i)\n",
        "    # run NMF\n",
        "    model = NMF(init=\"nndsvd\", n_components=i) \n",
        "    W = model.fit_transform(data)\n",
        "    H = model.components_    \n",
        "    k.append(i)\n",
        "    error.append(model.reconstruction_err_)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Applying NMF for k=2 ...\n",
            "Applying NMF for k=3 ...\n",
            "Applying NMF for k=4 ...\n",
            "Applying NMF for k=5 ...\n",
            "Applying NMF for k=6 ...\n",
            "Applying NMF for k=7 ...\n",
            "Applying NMF for k=8 ...\n",
            "Applying NMF for k=9 ...\n",
            "Applying NMF for k=10 ...\n",
            "Applying NMF for k=11 ...\n",
            "Applying NMF for k=12 ...\n",
            "Applying NMF for k=13 ...\n",
            "Applying NMF for k=14 ...\n",
            "Applying NMF for k=15 ...\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m-waFpIxxIwa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "outputId": "24305e9f-c167-4491-891a-ffd4074f42cf"
      },
      "source": [
        "# Plotting a bar graph to compare the results \n",
        "plt.plot(k, error) \n",
        "plt.xlabel('Number of dimensions', fontsize = 20) \n",
        "plt.ylabel('Reconstruction Error', fontsize = 20) \n",
        "plt.show() "
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q7rPltFljItN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "acfe6cff-5c04-4464-f06a-1961e7de828c"
      },
      "source": [
        "x = range(2, len(error)+2)\n",
        "\n",
        "from kneed import KneeLocator\n",
        "kn = KneeLocator(x, error, curve='convex', direction='decreasing')\n",
        "print(kn.knee)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yHN60HACjiUm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "c9f380b3-b730-4a78-c194-0d9d3ece14ff"
      },
      "source": [
        "plt.xlabel('Number of dimensions')\n",
        "plt.ylabel('Reconstruction error')\n",
        "plt.plot(x, error, 'bx-')\n",
        "plt.vlines(kn.knee, plt.ylim()[0], plt.ylim()[1], linestyles='dashed')"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7fb98de83610>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X7V0FPcUnJYM"
      },
      "source": [
        "# Lower dimensional cell embedding using NMF"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MS6bKTnQhlE7"
      },
      "source": [
        "optDim = kn.knee"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5IdCKmNLnCrd"
      },
      "source": [
        "#Mark the begining of the proposed method\n",
        "t.tic()"
      ],
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IGuo26QZd847"
      },
      "source": [
        "data_orig = data.copy()"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eu_ZcTpqcciX"
      },
      "source": [
        "model = NMF(n_components=optDim, init='nndsvd')\n",
        "W = model.fit_transform(data)\n",
        "H = model.components_"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CcpF1opmdIuX",
        "outputId": "a4b19fca-d119-46f1-9dde-ceb3e4aaa037"
      },
      "source": [
        "print(W.shape)\n",
        "print(H.shape)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(2544, 7)\n",
            "(7, 27828)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nvR7jYeGgue8"
      },
      "source": [
        "data = pd.DataFrame(W)"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AGKWL55oBiOS"
      },
      "source": [
        "# (A) Encoding labels (B) Labelling unknown cells as -1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GjHge5h94FLL",
        "outputId": "41526e23-a2b0-459d-ecb4-bf5ca7032e9f"
      },
      "source": [
        "print('Count of missing labels = ', sum(pd.isna(labels)))\n",
        "print('Percentage of missing labels = {0:.2f}'.format(sum(pd.isna(labels)/len(labels)*100)))"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Count of missing labels =  262\n",
            "Percentage of missing labels = 10.30\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jp-5v_bP33eF"
      },
      "source": [
        "index = labels.loc[pd.isna(labels)].index"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oqmPC-QJDdDA"
      },
      "source": [
        "**Encoding the labels**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z3U1_puTF7Wo"
      },
      "source": [
        "labels = labels.fillna('Unknown')"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yKJeGsbYDdDC"
      },
      "source": [
        "from sklearn import preprocessing\n",
        "le = preprocessing.LabelEncoder()\n",
        "y = pd.DataFrame(le.fit_transform(np.ravel(labels)))"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wbWGt5iPDdDG"
      },
      "source": [
        "y1 = y[0].copy()"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y_wSnX08V3vF"
      },
      "source": [
        "lab_dict = dict(zip(y[0], labels))"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jHkA-xmgDdDJ"
      },
      "source": [
        "**Labelling unknown data as -1**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AH2agqvhDdDO"
      },
      "source": [
        "dataWOmissingLab = data_orig.iloc[~y.index.isin(index)]\n",
        "LabNOTmissing = y.iloc[~y.index.isin(index)]"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HPSYXIQiDdDP"
      },
      "source": [
        "y.iloc[index] = -1           # setting Unknown labels as -1\n",
        "indx = pd.DataFrame(np.arange(0,data.shape[0]))\n",
        "df = pd.concat([data,indx], axis=1)\n",
        "X = pd.concat([df,y], axis=1)"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ifBE0rxBDdDR"
      },
      "source": [
        "#Setting k to the number of unique labels in the data excluding -1 (-1 stands for unknown labels)\n",
        "k = y[0].nunique()-1"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oryceblO3i7v"
      },
      "source": [
        "# Clustering using k-Means"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pd0KBJ1X3-N6"
      },
      "source": [
        "Recursive clustering"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I3VjKR_bCqzJ"
      },
      "source": [
        "def rec_KMeans(res):\n",
        "    if len(res) == 0:\n",
        "        return\n",
        "    \n",
        "    num_labels = set()\n",
        "    #finding no. of known labels for each cluster\n",
        "    for i in res:\n",
        "        if(i[-1] != -1):\n",
        "          num_labels.add(i[-1])\n",
        "    print(len(num_labels), num_labels)   \n",
        "\n",
        "    if(len(num_labels) == 1):     #if all labelled data belong from one class\n",
        "        final_clusters.append(res)\n",
        "        cluster_label.append(num_labels)\n",
        "        return\n",
        "    \n",
        "    if(len(num_labels) == 0):     #if no labelled data exist\n",
        "        final_clusters.append(res)\n",
        "        cluster_label.append(-1)\n",
        "        return\n",
        "    \n",
        "    #if all labelled data belong from more than one class, then cluster recursively\n",
        "    newk = len(num_labels)\n",
        "    centroid1 = []\n",
        "    rnd = random.sample(range(len(res)), newk)\n",
        "    for j in range(newk):\n",
        "        centroid1.append(res[rnd[j]])\n",
        "        \n",
        "    print('Partioning further...')\n",
        "    my_KMeans(res, centroid1, newk)"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qZlzPnBo4Blc"
      },
      "source": [
        "Passing each partition to recursive k-Means function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "khU9EUJq9uoT"
      },
      "source": [
        "def rec_KMeans_call(res):\n",
        "    for par in res:\n",
        "        print('...New cluster...')   \n",
        "        rec_KMeans(res[par])"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lLu1EVVT4ZoU"
      },
      "source": [
        "Distance between a given sample and a given centroid"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lSolb_2V4tXc"
      },
      "source": [
        "def distance(a,b):\n",
        "    ans = 0\n",
        "    for i in range(len(a)):\n",
        "        ans += math.pow((a[i] - b[i]),2)\n",
        "    return math.sqrt(ans)"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R-Wmt2QchgLI"
      },
      "source": [
        "def my_KMeans(data, centroid, k):  #using user-defined KMeans\n",
        "    \n",
        "    #max_iter = 1\n",
        "    #for i in range(max_iter):\n",
        "        \n",
        "    diction = {}    #empty dictionary to store data corresponding to each cluster\n",
        "    for i in range(k):\n",
        "        diction[i]=[]\n",
        "        \n",
        "    for j in range(len(data)):\n",
        "        l = []\n",
        "        for c in centroid:\n",
        "            l.append(distance(data[j][:-2],c[:-2]))      #calculate distance of the sample from each centroid\n",
        "        diction[l.index(min(l))].append(data[j])         #assigning the sample to the nearest centroid\n",
        "    \n",
        "    for c in diction:     #update centroids\n",
        "        if(len(diction[c])!=0):\n",
        "            centroid[c] = np.average(diction[c], axis = 0)\n",
        "    rec_KMeans_call(diction)"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BmRgi6qckASN"
      },
      "source": [
        "cntr = []\n",
        "final_clusters = []\n",
        "cluster_label = []"
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YxfW5witQ0MR"
      },
      "source": [
        "#Initializing centroids\n",
        "random.seed(0)\n",
        "rnd = random.sample(range(X.shape[0]), k)\n",
        "for i in range(k):\n",
        "        cntr.append(X.iloc[rnd[i]])"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "npTH-D9YS8vw",
        "outputId": "4c4d7271-d83f-4779-e6db-172d51deff0c"
      },
      "source": [
        "#initial k-Means call  \n",
        "my_KMeans(X.values, cntr, k)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "...New cluster...\n",
            "6 {0.0, 1.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "3 {0.0, 1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "5 {0.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "5 {0.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "5 {0.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {0.0, 1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "6 {0.0, 1.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "5 {0.0, 1.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "6 {0.0, 1.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "5 {0.0, 1.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {0.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "4 {1.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {1.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {1.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {1.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {1.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {1.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "5 {0.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "6 {0.0, 1.0, 2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {0.0, 2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {0.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "4 {0.0, 2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "4 {0.0, 1.0, 2.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "2 {2.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {0.0, 1.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "3 {0.0, 1.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {0.0, 1.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "3 {0.0, 1.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "2 {0.0, 1.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {1.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {0.0, 2.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "1 {0.0}\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {3.0, 4.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {2.0, 3.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "4 {2.0, 3.0, 4.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {4.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "0 set()\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {2.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "3 {2.0, 3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {2.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "2 {3.0, 5.0}\n",
            "Partioning further...\n",
            "...New cluster...\n",
            "1 {3.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n",
            "...New cluster...\n",
            "1 {5.0}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HTCGRRhEBoX7"
      },
      "source": [
        "# Results"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PtPaOvVhJzH9"
      },
      "source": [
        "Computing final centroids"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y7jFoyv4gWK0"
      },
      "source": [
        "def get_final_centroids(final_clusters):\n",
        "    final_centroids = []\n",
        "    for i in range(len(final_clusters)):\n",
        "        fc = pd.DataFrame(final_clusters[i]).iloc[:, :-2]\n",
        "        fc_mean = np.average(fc,axis = 0)\n",
        "        final_centroids.append(fc_mean)\n",
        "    return final_centroids\n"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MMAcmhYTJ45G"
      },
      "source": [
        "final_centroids = get_final_centroids(final_clusters)"
      ],
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "abofvkMGFEvo"
      },
      "source": [
        "def get_final_results(cluster_label):\n",
        "    no_of_points = []\n",
        "    labelled = []\n",
        "    unlabelled = []\n",
        "    cluster_lbl = []\n",
        "\n",
        "    dtf = [f'cluster{i}' for i in range(1,len(final_clusters) + 1)]\n",
        "    results = pd.DataFrame(dtf, columns = ['Clusters'])\n",
        "    \n",
        "    for i in cluster_label:\n",
        "        if( i != -1):\n",
        "            cluster_lbl.append(int(list(i)[0]))\n",
        "        else:\n",
        "            cluster_lbl.append(i)\n",
        "        \n",
        "    results['Label'] = cluster_lbl\n",
        "    \n",
        "    for i in range(len(final_clusters)):\n",
        "        no_of_points.append(len(final_clusters[i]))  #count of total samples\n",
        "        cl = 0\n",
        "        cu = 0\n",
        "        for j in final_clusters[i]:\n",
        "            if(j[-1] == -1):\n",
        "                cu += 1       #count of unlabelled samples\n",
        "            else:\n",
        "                cl += 1       #count of labelled samples\n",
        "        labelled.append(cl)\n",
        "        unlabelled.append(cu)\n",
        "\n",
        "    results['Total_Count'] = no_of_points\n",
        "    results['Count_ld'] = labelled\n",
        "    results['Count_ud'] = unlabelled\n",
        "    return results"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J5xmpi7VFIi8",
        "outputId": "4a16af45-e7e4-4186-cb83-db23281d76f4"
      },
      "source": [
        "result = get_final_results(cluster_label)\n",
        "print(result)"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       Clusters  Label  Total_Count  Count_ld  Count_ud\n",
            "0      cluster1      4          137       134         3\n",
            "1      cluster2      0            1         1         0\n",
            "2      cluster3      4            1         1         0\n",
            "3      cluster4      4            4         3         1\n",
            "4      cluster5     -1            2         0         2\n",
            "..          ...    ...          ...       ...       ...\n",
            "595  cluster596      3            1         1         0\n",
            "596  cluster597      5            1         1         0\n",
            "597  cluster598      5            2         2         0\n",
            "598  cluster599      5            2         2         0\n",
            "599  cluster600      5            3         3         0\n",
            "\n",
            "[600 rows x 5 columns]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BqFWlR1qvVCO"
      },
      "source": [
        "# Labelling clusters with both labelled and unlabelled cells"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "goZgzvQtfjJ4"
      },
      "source": [
        "pl=[]\n",
        "index=[]\n",
        "\n",
        "for i in range(len(result)):\n",
        "    cls = result['Label'][i]\n",
        "    nud = result['Count_ud'][i]\n",
        "    if cls != -1 and nud > 0:\n",
        "        for j in final_clusters[i]:\n",
        "            if(j[-1] == -1):\n",
        "                j[-1] = cls   #setting the class label\n",
        "                #marking the predicted label and corresponding index position\n",
        "                id = int(j[-2])\n",
        "                index.append(id)     \n",
        "                pl.append(cls)"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U3Q8N2fxGKnj"
      },
      "source": [
        "# Setting weighted radius of clusters as threshold"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AAMpwb35CLqT"
      },
      "source": [
        "rad=[]\n",
        "for i in range(len(final_centroids)):\n",
        "    dist=[]\n",
        "    for j in final_clusters[i]:\n",
        "        dist.append(distance(final_centroids[i],j[:-2]))\n",
        "    rad.append(np.max(dist))"
      ],
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a_qE4ma8Kzfd"
      },
      "source": [
        "wrad=0\n",
        "npnts=data.shape[0]\n",
        "for i in range(len(final_clusters)):\n",
        "    wrad += rad[i]*len(final_clusters[i])\n",
        "wrad/=npnts"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E9VcM6nqJ_3S"
      },
      "source": [
        "# Labelling the clusters with all unlabelled cells"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_lP4YswZ6KDV"
      },
      "source": [
        "pos = [i for i in result.loc[result['Label']==-1].index]"
      ],
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MGpzeKbP_g-r",
        "outputId": "ad405249-3581-49a7-98f1-98f5ab2e0194"
      },
      "source": [
        "d = euclidean_distances(final_centroids, final_centroids)\n",
        "for i in pos:\n",
        "    nc = i\n",
        "    #find nearest labelled cluster\n",
        "    while result.loc[nc,'Label'] == -1:\n",
        "        d[i][nc]=999\n",
        "        nn = np.where(d[i] == np.amin(d[i]))  #finding nearest neighbor of the unlabelled cluster\n",
        "        nc = nn[0][0]\n",
        "\n",
        "    #Setting labels of unlabelled data in unlabelled clusters to the class label of the nearest cluster\n",
        "    #if distance from nearest centroid is less than or equal to threshold distance (weighted radius)\n",
        "    l = len(final_clusters[i])  #number of points in cluster i\n",
        "    print('no. of points in cluster {0}: {1}'.format(i,l))\n",
        "    c=0\n",
        "    for j in final_clusters[i]:\n",
        "        if (distance(final_centroids[nc],j[:-2]) <= wrad):\n",
        "            c+=1\n",
        "            j[-1] = result['Label'][nc]   #setting the class label\n",
        "            #marking the predicted label\n",
        "            id = int(j[-2])\n",
        "            index.append(id)\n",
        "            pl.append(int(j[-1]))\n",
        "    print('no. of points labelled now: ',c)\n",
        "    if c==l:    #implies labels of all samples in cluster i changed\n",
        "        print('Label of cluster {0} changed to the label of its nearest neighbour cluster {1}'.format(i+1,nc))\n",
        "        result.loc[i,'Label'] = result.loc[nc,'Label']"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no. of points in cluster 4: 2\n",
            "no. of points labelled now:  2\n",
            "Label of cluster 5 changed to the label of its nearest neighbour cluster 6\n",
            "no. of points in cluster 7: 2\n",
            "no. of points labelled now:  2\n",
            "Label of cluster 8 changed to the label of its nearest neighbour cluster 4\n",
            "no. of points in cluster 13: 2\n",
            "no. of points labelled now:  1\n",
            "no. of points in cluster 59: 2\n",
            "no. of points labelled now:  0\n",
            "no. of points in cluster 81: 3\n",
            "no. of points labelled now:  3\n",
            "Label of cluster 82 changed to the label of its nearest neighbour cluster 94\n",
            "no. of points in cluster 132: 1\n",
            "no. of points labelled now:  1\n",
            "Label of cluster 133 changed to the label of its nearest neighbour cluster 202\n",
            "no. of points in cluster 174: 1\n",
            "no. of points labelled now:  1\n",
            "Label of cluster 175 changed to the label of its nearest neighbour cluster 175\n",
            "no. of points in cluster 224: 1\n",
            "no. of points labelled now:  1\n",
            "Label of cluster 225 changed to the label of its nearest neighbour cluster 222\n",
            "no. of points in cluster 266: 9\n",
            "no. of points labelled now:  8\n",
            "no. of points in cluster 335: 1\n",
            "no. of points labelled now:  1\n",
            "Label of cluster 336 changed to the label of its nearest neighbour cluster 338\n",
            "no. of points in cluster 345: 3\n",
            "no. of points labelled now:  1\n",
            "no. of points in cluster 540: 1\n",
            "no. of points labelled now:  1\n",
            "Label of cluster 541 changed to the label of its nearest neighbour cluster 541\n",
            "no. of points in cluster 572: 1\n",
            "no. of points labelled now:  1\n",
            "Label of cluster 573 changed to the label of its nearest neighbour cluster 574\n",
            "no. of points in cluster 581: 2\n",
            "no. of points labelled now:  1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RaE5-BUUo_Cw"
      },
      "source": [
        "Computing running time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0oJc1pdGnZDO",
        "outputId": "8a2d6f09-3c6b-4489-8300-69bc64ce5f71"
      },
      "source": [
        "#Compute time elapsed at the end of proposed algorithm\n",
        "t.toc()"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Elapsed time is 66.921820 seconds.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pHIgvGm92PMt"
      },
      "source": [
        "# Results after reassignment"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G1alCbK337zp"
      },
      "source": [
        "def get_final_results(result):\n",
        "    labelled = []\n",
        "    unlabelled = []\n",
        "    for i in range(len(final_clusters)):\n",
        "        cl = 0\n",
        "        cu = 0\n",
        "        for j in final_clusters[i]:\n",
        "            if(j[-1] == -1):\n",
        "                cu += 1       #count of unlabelled samples\n",
        "            else:\n",
        "                cl += 1       #count of labelled samples\n",
        "        labelled.append(cl)\n",
        "        unlabelled.append(cu)\n",
        "\n",
        "    result['Count_ld_Now'] = labelled\n",
        "    result['Count_ud_Now'] = unlabelled\n",
        "    return result"
      ],
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Vlh_td882H32",
        "outputId": "bdfb92cc-1517-4564-df6b-ddc763a6cc8e"
      },
      "source": [
        "reassignmentResult = get_final_results(result)\n",
        "print(reassignmentResult)"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       Clusters  Label  Total_Count  ...  Count_ud  Count_ld_Now  Count_ud_Now\n",
            "0      cluster1      4          137  ...         3           137             0\n",
            "1      cluster2      0            1  ...         0             1             0\n",
            "2      cluster3      4            1  ...         0             1             0\n",
            "3      cluster4      4            4  ...         1             4             0\n",
            "4      cluster5      4            2  ...         2             2             0\n",
            "..          ...    ...          ...  ...       ...           ...           ...\n",
            "595  cluster596      3            1  ...         0             1             0\n",
            "596  cluster597      5            1  ...         0             1             0\n",
            "597  cluster598      5            2  ...         0             2             0\n",
            "598  cluster599      5            2  ...         0             2             0\n",
            "599  cluster600      5            3  ...         0             3             0\n",
            "\n",
            "[600 rows x 7 columns]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ApHYk-t7d_Hp",
        "outputId": "497d1b0c-1013-4804-dd00-ab30feff1dfb"
      },
      "source": [
        "#Finding how many samples are still unlabelled\n",
        "count = 0\n",
        "unlab = []\n",
        "for i in range(len(final_clusters)):\n",
        "  for j in final_clusters[i]:\n",
        "    if(j[-1] == -1):\n",
        "      count+=1\n",
        "      unlab.append(int(j[-2]))\n",
        "print('Count of unlabelled cells: ', count)\n",
        "print('Percentage of unlabelled cells: {0:.2f}'.format(count/data.shape[0]*100))\n",
        "if count>0:\n",
        "  print('Unknown cell indices: ',unlab)"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Count of unlabelled cells:  7\n",
            "Percentage of unlabelled cells: 0.28\n",
            "Unknown cell indices:  [1292, 1377, 1389, 98, 1262, 1436, 1429]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NSnaLIdM9cpF"
      },
      "source": [
        "#Remove unpredicted cells from data\n",
        "index_labelled = ~data_orig.index.isin(unlab)\n",
        "data_labelled = data_orig.iloc[~data_orig.index.isin(unlab)]"
      ],
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sMcn54eBglRo"
      },
      "source": [
        "labWOmissing = pd.DataFrame(list(zip(LabNOTmissing.index,LabNOTmissing[0].values)), columns = ['Index', 'Predicted Label'])"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kGtd9NyBapEJ"
      },
      "source": [
        "predicted = pd.DataFrame(list(zip(index, pl)), columns = ['Index', 'Predicted Label'])"
      ],
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SwLtK4X0gcZ2"
      },
      "source": [
        "allLabels = pd.concat([labWOmissing, predicted], axis=0).sort_values(by = 'Index')"
      ],
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iWiPdGtCqVvq"
      },
      "source": [
        "**Cohesion and separation of clusters with newly predicted predicted cells added**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tFTdARfsg54C",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bb45ac17-983c-489f-9b50-801414ad34e9"
      },
      "source": [
        "#for data with newly predicted cells added\n",
        "print('Internal indices for data including newly predicted cells (After Clustering):  \\n')\n",
        "print('Calinski Harabasz Score: {0:.2f}'.format(calinski_harabasz_score(data_labelled, allLabels['Predicted Label'].values)))"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Internal indices for data including newly predicted cells (After Clustering):  \n",
            "\n",
            "Calinski Harabasz Score: 21.30\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dlpanaNnFPI-"
      },
      "source": [
        "# -----------THE END----------"
      ]
    }
  ]
}